What kind of purpose are you talking about? He does not simply run willy nilly outside all day. He is inside except for potty breaks and he is very very lazy inside. Even outside he is not destructive towards property or objects-and has never acted "puppy-like."
I do take him on jogs a few times a week. I have trails on my property with lots of hills and trees. He is great for that but tires out very quickly. There aren't any other people or dogs that far back, but as stated I haven't taken him to the park too much after this started.
I'm not sure if this was meant to be offensive- but I don't think I've portrayed myself to be an owner unwilling to put in time or work? If that was the case I wouldn't have sought help for both myself and him.
I got the fence for my dogs solely for a more enjoyable purpose for them, and it was recommended to me.
Did not mean for this to be offensive, and it was written before I had re-considered and had Idea B.
I am suspecting that he has associated the cats/Labrador/horses/alpaca with getting hurt by the fence collar. Particularly if he started out as not confidant (frightened of the neighbor's dog), the correction from the collar may have confirmed that the other animals are dangerous to him and he has gone into self-defence mode ("I must get you before you can get me"). This is sometimes the down side of electronic containment, and one of the reasons I don't much like e-fences.
If it is O.K. with you, I am going to put this out on a training list with lots of seriously talented e-collar trainers. I am sure there is some sort of protocol for un-doing his having gone to this place in his head, but I do not know what it is. I will let you know after I have gotten some feedback.
In the meantime, I would prevent the running. If he slipped out of a martingale (grayhound collar), than it was not fitted properly... when it is high up on his neck and there is tension on the leash, there should be a gap of maybe a couple of inches between the ends of the larger part of the collar where the martingale part goes (does this make sense?)... if he slipped it, it was too loose. I would not use a pinch collar... he is trying to keep the electronic fence from biting him, and substituting another hurt is not going to help.